Families' Use of Payment Instruments During
a Decade of Change in the U.S. Payment System

In the U.S., the share of payments made "electronically" --with
credit cards, debit cards, and direct payments--grew from 25
percent in 1995 to over 50 percent in 2002 (BIS, 2004). This paper
frames this aggregate change in the context of individual behavior.
Family level data indicate that the share of families using or
holding these instruments also increased over the same period. The
personal characteristics that predict use and holdings are
relatively constant over time. Furthermore, the results indicate
that the aggregate change may be correlated with a greater
incidence in "multihoming", or use of multiple payment instruments.
In addition, the paper offers evidence that the dimensions over
which families multihome differ across payment instruments. The
results presented in this paper document a significant change in
the payment system, inform payment system policies, and provide
evidence of technology adoption behavior more generally.

JEL codes: G20, D12, E41.

Introduction

In the 1950s, most consumers paid by either cash or check. Both
of these are paper-based forms of payment. Financial innovation
from the 1970s to today created new electronic ways for individuals
to pay, such as debit cards, credit and charge cards, and direct
payments from a bank account. Despite these innovations, many
families continued to rely significantly on paper payments through
the early 1990s. However, in the mid-1990s and early 2000s, a major
shift in the U.S. payment system occurred. The share of consumer
payments made with electronic devices such as credit cards, debit
cards and direct payments jumped from 25 percent in 1995 to over 50
percent in 2002 (BIS, 2004).

This paper investigates the link between aggregate changes in
the use of different forms of payment to family level survey data
on payment systems. Family level data from the 1995, 1998 and 2001
waves of the Survey of Consumer Finances (SCF) indicate that the
share of families using or holding electronic forms of payment also
increased over the same period. In addition, the proportion of
families using more than one payment instrument also moved up, a
practice called "multihoming." The results in this paper document a
significant change in the payment system, inform payment system
policies, and provide evidence of technology adoption behavior more
generally.

Previous research using the SCF data shows that payment
instrument use is significantly correlated with income, age and
demographic characteristics (Kennickell and Kwast (1997), Stavins
(2001), Mester (2003) and Hayashi and Klee (2003)). Importantly,
this paper extends previous results in three ways. First, it
documents these relationships over a time of significant change in
the payment system. Second, it explores the correlation between the
use of different payment instruments, which lends insight into the
complementarity or substitutability of different payment
instruments. And finally, it discusses the rise in multihoming.

There are three important reasons to study payment system
issues. First, payment systems are a huge, important component of a
well-functioning market economy. In 2002, there were approximately
82 billion payments valued at $65 trillion dollars made with
checks, credit cards, debit cards, and automated clearing house
(ACH) payments.2 These payment flows were over six times
the dollar value of GDP, and more than $225,000 per capita. Second,
paper payments are more resource intensive than electronic
payments, and these resource costs represent anywhere from 1/2 to 3
percent of GDP (Humphrey and Berger (1990), Wells (1996), Hahn
(2004)). Thus, a change in the payment system that causes a shift
away from paper to electronic payments could potentially save
resource costs, thereby increasing economic efficiency. And third,
payment systems have been the subject of multiple antitrust cases
and policy initiatives. The results on the substitutability of
different payment instruments could help inform policymakers on the
potential effects of payment system policies on consumer
behavior.

To preview the results, there has been significant increases in
the proportion of families who report using debit cards and direct
payments. Age and income are strongly correlated with the decision
to use these particular payment instruments. Younger families and
higher income more frequently report using a debit card or direct
payments. These results point to possible effects of the propensity
to adopt new technologies or access to new technologies in a
family's decision to use electronic forms of payment. Personal
characteristics have a large influence on the type of payment
instruments used.

At the same time that the proportion of families using debit
cards and direct payments grew, however, the proportion of families
that report using checks or holding credit cards has remained
relatively stable. This observation leads to the next part of the
analysis, that is, to investigate how multihoming behavior has
changed over the period. Indeed, the share of families that
multihome increased substantially. The factors that determine
multihoming behavior are generally the same that determine
electronic payment use. Income, age, and demographics tend to be
correlated with multihoming behavior. This result leads us to
believe that while families adopted new forms of payment, they did
not immediately stop using the older forms of payment. Payment
choice likely depends on the nature of the transaction.

Given that families choose individual payments based on their
demographic characteristics, and likely choose within a portfolio
of payment instruments for any particular transaction, it is
natural to investigate this multihoming behavior more closely.
Although the final set of results are a bit difficult to interpret,
they seem to suggest that families generally use both debit cards
and credit cards together. However, by refining the categories
somewhat, it appears that families either use debit cards or they
are convenience users of credit cards, but usually not both.
Similarly, debit card use is an either-or decision with direct
payment use. No apparent pattern can be distinguished for debit
card and check use, or direct payment and check use.

These results help us understand the aggregate trends in the use
of noncash payments. Because aggregate data indicate that the
number of electronic payments increased while the number of check
payments declined, while the family level data indicate that the
use and holdings of these payment instruments either held steady or
did not fall, families likely changed their intensity of use of
different payment instruments. Although the data offer little
indication of intensity of use, understanding factors that may
contribute to multihoming behavior helps inform ongoing theortical
research that models this phenomenon.3 Taking the family-level results
together with the aggregate results, we can get a sense of how the
change in family behavior over this period affected the aggregate
number of payments overall.

One caveat is that this paper addresses demand influences only.
To be sure, supply-side factors also contributed to the shift from
paper to electronic payments. Many of the networks and a large part
of the technical infrastructure that supply electronic payments
were established before 1995. But, although the backbones of these
networks existed before 1995, access points increased substantially
from 1995 to 2001. One notable increase was in the number of point
of sale terminals for PIN debit cards. In 1995, there were
approximately 530,000 terminals; in 2001, 3.64 million (BIS,
various years). Whether this was a cause or an effect of increased
adoption rates by families is difficult to determine, but it is not
surprising that the two phenomena occurred during the same period.
Although this paper focuses on demand factors at the consumer
level, these supply-side influences should be noted.

The paper proceeds as follows. Section 2 gives extensive background on the U.S. payments
system, including a brief history, aggregate statistics, and
family-level statistics. Section 3 posits a
theoretical model of payment choice and describes the estimation
procedure. This leads to the estimation results reported in section
4. Section 5
offers conclusions and suggestions for further research.

Background on the U.S. payments system

History

Today consumers pay for goods and services with cash and
"noncash retail payments" - debit cards, credit and charge cards,
direct payments from a bank account, known as automated clearing
house (ACH) payments, and check payments. Debit card, ACH and
checks deduct money directly from a user's account. In contrast,
credit cards provide users with a line of credit, either revolving
or non-revolving (also known as charge cards). This study focuses
on these noncash retail payments, because data on cash use is
generally unavailable.4

A quick overview of payment system history gives perspective on
the aggregate data. The payment instruments commonly used today
developed at different points in time. The oldest type of noncash
retail payment commonly used by U.S. consumers today is the check.
The earliest forms of check payments were introduced in the late
1600s, and until relatively recently, represented the great
majority of noncash retail payments.5 In fact, in the 1960s, concern grew
over a projected dramatic increase in the number of check payments,
which led to the development of the ACH, a computer-based system
for payments available to consumers. Common uses of the ACH include
direct deposit of payroll, mortgage payments, utility bill payments
and insurance payments. The number of payments made with the ACH
increased substantially throughout the 1980s and 1990s, and the
value of these payments also continues to increase.

"Plastic" payment instruments developed in the second half of
the twentieth century. The first general purpose charge card,
Diners Club, was introduced in 1950. Before the 1950s, some
retailers offered "charga-plates", but these were limited to a
particular establishment. Credit cards were not widely used until
the 1970s, and use grew across the income distribution through the
1980s and 1990s.6 The earliest forms of debit cards
appeared in the 1970s.7 Although debit card use was relatively
nonexistent before 1989, by 2001, almost one half of U.S. families
used a debit card. An indication of debit card's current prominence
is that Visa reported in 2002 that more transactions on their
network were made with debit cards than with credit cards; this
trend continues through today.8

Over the history of U.S. payment system, there have been few
periods during which payment patterns changed as dramatically as
over the past ten years. Through the 1960s, consumers relied
heavily on cash, checks and store credit as the primary means of
payment. Payment patterns started to shift in the 1960s through the
1970s, when credit cards and direct payments began to be used
widely, although the share of noncash payments made by check
remained high. At the end of this period, in 1979, checks
represented 85.7 percent of noncash retail payments.9
In the sixteen years between 1979 and 1995, the share of noncash
payments made electronically grew 9 percentage points. Since 1995,
this share grew rapidly, almost tripling in only eight years.

Today, electronic payment networks are growing in importance in
the U.S. economy. For some economic activity, electronic payment
networks are critical, such as for e-commerce. Data from the U.S.
Census Bureau show that retail e-commerce sales increased from $6.1
billion in the fourth quarter of 1999 to $15.5 billion in the first
quarter of 2004, which represents an increase from 0.7 percent of
total retail sales to 1.9 percent. It is likely that a large chunk
of consumer Internet shopping goes through the Visa and MasterCard
networks, and a good portion of business-to-business e-commerce
eventually flows through the ACH network. 10

Aggregate and family-level data

Aggregate data

The history of the payment system offers a backdrop for better
understanding data on the most common payment instruments in use
today. Tables 1(a) and 1(b) show data on noncash retail payments
from 1995 to 2001. Table 1(a) shows the total number of noncash
retail payments; the left side shows number and the right side
shows shares. The total number of noncash retail payments grew from
approximately 65.7 billion in 1995 to 78.8 billion in 2001.
Concurrently, the estimated number of checks paid fell from 49.5
billion in 1995 to 41.2 billion in 2001.11 With an assumed 3 percent annual
decline, the number of checks paid fell to 41.2 billion in
2001.

The right half of the table shows the share of the number of
noncash retail payments of each payment type. The share of the
number payments made by debit card increased 13 percentage points,
from 3 percent in 1995 to 16 percent in 2001. The credit card share
increased 5 percentage points, and the ACH share increased 5
percentage points. At the same time, the estimated check share fell
from 75 percent in 1995, to 57 percent in 2000, to 52 percent in
2001. Overall, the share of payments made electronically increased
23 percentage points, from approximately 25 percent in 1995 to 48
percent in 2001.

Table 1(b) shows the value and shares of constant-dollar noncash
retail payments. Check and ACH payments represent relatively larger
shares of the value of payments than the share of the number of
payments. This is mainly because debit cards and credit cards are
used primarily to purchase smaller value items at the point of
sale, whereas checks and ACH may be used to pay mortgages,
salaries, and other higher-dollar value payments. Consistent with
this view, while debit card's share of the number of payments
increased 8 percentage points from 1998 to 2001, its share of the
value of payments increased only one percentage point.12

Survey of Consumer Finances

The trend towards electronic payment evident in the aggregate
are also in household data from the Survey of Consumer
Finances.13 According to the SCF, families' use of
debit cards, credit cards and ACH payments grew substantially from
1995 to 2001.14 Table 2(a) presents payment use and
holdings statistics from the complete SCF samples. As shown in line
1 of the table, from 1995 to 2001, debit card use increased 29.4
percentage points, from 17.6 percent of families in 1995 to 47.0
percent of families in 2001. As shown in lines 3 and 4 of the
table, there has also been a rise in debit card use among those who
do not have a checking account, likely because government benefit
programs increasingly use debit cards or similar payment
instruments as a method for disbursing funds to program recipients.
Thus, it appears that the use of debit cards have increased across
the income distribution.

The broad increase in debit card use across different income and
age groups is shown clearly in figures 1(a) and 1(b). The x axis in
each of these figures plots the group of families, and the y axis
plots the use of debit cards as a percentage of that group. The
three lines represent data from the 1995, 1998 and 2001 waves of
the survey. As shown in figure 1(a), debit card use rises, then
falls with income. In contrast, as shown in figure 1(b), debit card
use steadily falls with age. However, in both cases, there was a
level rise across all groups in debit card use. The aggregate rise
in the number of debit card transactions may be able to be
explained in part by these family trends.

From 1995 to 2001, the fraction of households with credit cards
increased 1.8 percentage points, to 76.2 percent of families. The
relatively slight increase in total holdings masks a change in
composition: "Bank" credit card holdings, or cards issued on the
Visa, MasterCard, Discover networks, or American Express' Optima
credit card, increased 6.3 percentage points while retailer card
holdings decreased 12.4 percentage points and gas card holdings
decreased 8.6 percentage points. In addition, the proportion of
"convenience users" - families who had new charges on their last
bill and had no balance after the last payment was made on the
account - increased 4.1 percentage points from 1995 to
2001.15 This represents a growing proportion
of bank credit card users overall. In 1995, convenience users were
36.8 percent of bank credit card holding families; in 1998, 37.2
percent, and in 2001, 39.3 percent. American Express, Diners Club,
or Carte Blanche card holdings (commonly referred to as travel and
entertainment charge cards), stayed relatively constant, at 11.0,
9.1 and 10.6 percent of families in 1995, 1998 and 2001,
respectively.

Figures 2(a) and 2(b) graphically present how credit card
holdings vary by income and age. Unlike with debit card use, credit
card holdings steadily increase with income. In all survey years,
over 95 percent of families in the top tenth of the income
distribution had a credit card. Part of this difference may stem
from the need to satisfy certain measures of credit worthiness in
order to obtain a credit card; higher income families may be more
likely to satisfy these requirements. Also, as indicated in figure
2(b), the incidence of credit card holdings tends to rise, then
fall, with age, showing the highest rates of credit card use are
among working-age families.

Direct payment use also increased over this period. From 1995 to
2001, direct payment use increased 18.5 percentage points, to 40.3
percent of families. Many industries that receive recurring
payments from their consumers have adopted the use of the ACH.
According to the survey data, families most frequently reported
that they use direct payment for insurance premiums across all
survey years.

However, not every bill can be paid with a direct payment, and
not all other payments can be made with either a credit card or
debit card. Thus, despite these increases in use and holdings of
electronic forms of payment, as shown in the last line of the
table, the share of families that reported using checks as a main
way of interacting with a financial institution remained stable at
approximately 75 percent of families.16 This result suggest multihoming by
families.

Indeed, many families use or hold more than one type of payment
instrument, and the proportion of families using or holding more
than one increased over time. Table 2 (b) gives summary statistics
on the proportion of families that use or hold more than one of
these instruments. As shown in the table, in 1995, 14.5 percent of
families used a debit card and had a credit card. This share
increased to 37.8 percent of families in 2001, a jump of 23.3
percentage points. Similarly, the share of families that used a
debit card and direct payment also jumped, from 5.6 percent of
families to 23.2 in 2001. The proportion of families using debit
cards, holding credit cards, and using direct payment increased
15.2 percentage points, from 4.8 percent of families in 1995, to
20.0 percent of families in 2001.

However, evidence suggests that not all families multihome in
the same way. Table 2 (c) reports cross-tabulations of credit card
and debit card use in 2001. These statistics show that not only do
families use more than one type of card, families use these cards
differently. The data are broken up into four categories of credit
card users: convenience users, or bank credit card holders who had
new charges, but no balance owed after the last bill was paid on
the account; borrowing users, or bank credit card holders who had
new charges, and had a balance owed after the last bill was paid on
the account; only holding, or bank credit card holders who had no
new charges on the account, and borrowing nonusers, or bank credit
card holders who had no new charges, and had a balance owed after
the last bill was paid on the account.

Interestingly, while only about 44 percent of families who use
credit cards for convenience use a debit card, approximately 59
percent of families who borrow on credit cards use a debit card.
Borrowing non-users, defined as families who reported outstanding
credit card balances but did not report any new charges report a
similar percentage of debit card use to borrowing users of credit
cards, approximately 58 percent. According to Visa and MasterCard
rules at the time these data were gathered, there was no difference
for retailer acceptance of a bank credit card or a signature debit
card transaction. In addition, many debit cards have both
functionalities: they allow consumers to sign or to use a PIN.
These features mitigate supply-side factors that could affect the
choice between debit and credit. Possible explanations include use
of a debit card as a device to discipline spending or credit
constraints for borrowing users.17

To summarize, from 1995 to 2001, the number of electronic
payments increased by approximately 20 percent. The aggregate
statistics show that the share of payments made with debit cards,
credit cards and ACH payments steadily increased from 1995 to 2001,
while the share of payments made by check fell. At the same time,
the family-level data indicate that the proportion of families that
used debit cards and direct payments increased, and the proportion
of families that had credit cards or used checks stayed relatively
constant. Means of the survey data suggest that use of these
payments appear to differ by income, demographics and purpose of
payment. These statistics motivate the model presented in the next
section, which formalizes a consumer's choice of payment instrument
based on personal characteristics and the nature of the
transaction. The model then leads to the estimation procedure,
which presents the assumptions needed in order to estimate the
model accurately.

The model and estimation procedure

Model of payment instrument choice

Consider a situation where a consumer decides what payment
instrument to use. One set of factors that may influence a decision
is personal characteristics. As noted in the introduction, previous
research has shown that age, income, and demographic
characteristics are correlated with use of payment instruments.
These factors could proxy for access to different payment
instruments, willingness to try new products, and the cost of the
payment technology relative to other payment technologies.

Another set of factors that should also influence choices are
the characteristics of the payment instrument itself. Some card
products offer consumers airline miles or cash back bonuses when
they are used. Other people may prefer checks, as checks could be
perceived to help consumers with budgeting or accounting.18 Most direct payments from a bank
account are originated on a recurring, regularly scheduled basis
and may only require the consumer to sign up for the service
once.

A third set of factors that may influence a consumer in making
payment choices are the characteristics of transactions. For
example, credit cards are convenient to use for many purchases made
on the Internet. Checks, in contrast, may be less convenient for
some types of Internet transactions, but more convenient for casual
payments, for example to an individual or to a small business.
Direct payments are convenient for a regularly scheduled payment -
such as a mortgage - but cumbersome for Internet purchases or for
paying indivuduals.

Given these sets of factors, the model specified assumes that
the consumer chooses the payment instrument that maximizes utility,
specified as

(1)

where is
family 's utility for
payment instrument for
transaction type ,
is a vector of
family characteristics,
is a vector of payment instrument characteristics and is a vector of transaction
characteristics. ,
and are vectors of parameters that
weight these factors in the consumer's utility function.

A common approach in estimating discrete choice models is to
assume that some factors that determine payment choice are
unobserved by the econometrician. The utility of the consumer is
then specified as

(2)

where
captures
the unobserved factors. In addition, the researcher observes an
indicator that
equals one if consumer
chooses payment instrument for transaction . Assuming a probability distribution for the
unobserved factors that determine payment choice leads to a
probability of using or having a particular payment instrument
based on observed factors. If the probability distribution
satisfies certain properties, McFadden (1973) shows that this
specification satisfies the properties necessary and sufficient to
be consistent with utility maximization.

Assuming that the error terms are independently and identically
distributed with an extreme value distribution, the probability
that a family chooses a particular payment instrument is

where
and
is the cumulative
distribution function of the error term. In the estimation that
follows, different distributional assumptions for the error term -
normal and logistic - will determine the numerical
probabilities.

As a final note, the consumer chooses the payment instrument
most appropriate for each transaction. This captures the idea that
consumers may consider a debit card transaction for a grocery store
purchase different from a debit card transaction for a mortgage
payment. If it is assumed that consumers make more than one type of
transaction, and thus make more than one decision, it is likely
that consumers use more than one type of payment. Differentiating
the decisions by both payment instrument and transaction type
allows the model to capture the multihoming seen in the data.

Estimation procedure

Due to data limitations, not all of the parameters of the model
in (2) can be estimated. Advantages of the SCF
include its well-documented and rigorous sampling structure and its
extensive demographic characteristics; disadvantages include the
lack of information on factors that may influence payment choice.
To start, the data do not contain information on attributes of
different payment instruments available to the consumer. For
example, there is no information on fees charged for debit card
use, ACH payment use, or per-check fees. These fees likely affect
consumer payment choices.

Another data limitation is that the SCF does not ask questions
that would be useful to determine the influence of transaction
characteristics. Although the data include information on whether
the family uses a debit card, for example, there is no information
on where they use the debit card. Families may choose to use debit
cards relatively more often at grocery stores than at restaurants
because, in general, grocery stores have PIN pads and restaurants
do not.

In addition, the econometrician does not observe the supply side
- the financial institutions' decisions on what types of payment
instruments to offer families. Although the SCF does contain some
information on past bankruptcies - which could lend insight into
credit constraints - and information on credit card interest rates
- which could proxy for the riskiness of the borrower - including
these in the estimation may introduce bias in the estimates and
thus may not be a good proxy for supply concerns.

But, as noted elsewhere, data on payment systems are
scarce.19 Thus, the advantages of using the SCF
to study payment choice outweigh the disadvantages detailed above.
However, the data limitations will influence the estimation
procedure.

In particular, the data limitations imply that the model must be
estimated on the vector of consumer characteristics only. The lack
of fee or other relevant data related to payments noted above
implies that there is no variation in the data for the choices,
only variation across families. Essentially, the estimated
parameters are family characteristic hedonics for using or holding
particular payment instruments.

Thus, in order to estimate the effect of different
characteristics on payment choice, one must construct parameters
for each characteristic specific for each choice. The coeffiecients
in equation
(2) become . Because utility is a relative concept, adding
the same constant to the utility of each choice does not alter the
family's decision problem. This feature makes it necessary to
normalize the coefficients relative to one of the possible
outcomes.

However, there is still a need to capture three things in the
data: the rise in the use of electronic payment, the incidence of
multihoming, and the substitutability of different payment
instruments. There are three estimation procedures used to tackle
these problems. The first model is a simple binomial model that
evaluates the probability of using or holding different payment
instruments. Estimates of this model provide one parameter set,
which reflects the probability of using or holding the particular
payment instrument, relative to not using or holding the payment
instrument. For this model, a normal distribution for the
unobserved error term in (6) is
assumed. With this assumption, the log-likelihood function of
given
is

(7)

where is an
indicator that consumer
uses or holds payment instrument and is
the normal cumulative distribution function. Note that this
specification implies that transaction characteristics are subsumed
in the error term.

The second model fits an ordered probit model, which uses the
count of the number of different payment instruments used as the
dependent variable. The values of the count range from zero to
four. No distinction is made between using different combinations
of payment instruments; rather, this model gives insight into the
decision to hold multiple payment instruments. Because families
choose a payment instrument for each transaction, the payment
instrument chosen must yield the maximum utility. Aggregating these
maxima over the set of transactions should preserve the fundamental
utility ordering. Thus, the utility concept remains fundamentally
the same as in the binomial model.

Let

(8)

where is the number of
payment instruments available to families. is a number between zero and four.
Also, let
denote
boundary values that correspond to the counts of payment
instruments, and let
be probabilities defined as

This model implies the choice probabilities given as

(9)

Setting equal
to one implies the log-likelihood of
given
is

(10)

where is an
indicator function that equals one if .

Because the ordered probit model does not give insight into the
most preferred combinations of payment instruments, the third model
examines the multiple payment instrument decision a bit more
closely and evaluates how families substitute one payment
instrument for another. Four models are specified: debit and
credit, debit and convenience user, debit and check, and debit card
and direct payment. The different pairings allow evaulation of the
dimensions over which families perceive payment instruments to be
substitutes or complements. Debit cards and credit cards are
physically similar and can often be used at the same types of
locations. However, they potentially have very different effects on
a family's balance sheet. Comparing debit cards and convenience use
of credit cards gives perspective on the use of credit cards simply
for transactions, and not for exensions of credit. Debit cards and
checks provide insight into newer versus older forms of payment
that act directly on a bank account and can be used at the point of
sale, while debit cards and direct payment elucidate electronic
payment adoption behavior.

Both multinomial logit models and nested multinomial logit
models are estimated. Tests are performed to see whether the
multinomial assumptions are adequate to answer the research
question, as the multinomial logit model is a special case of the
nested multinomial logit model. The probability of choosing a
combination of payment instruments is specified as

(11)

where denotes the
combination of payment instruments chosen by family , subscripts all the nests, , and defines the degree of
substitutability within the nest. If equals one, the model collapses to the
multinomial logit model. Whether this is the case is an empircal
question we explore later in the estimation results.

Estimation results

The subsample used in the estimation procedure eliminates
families with no income, zero or negative assets, and no affiliated
financial institutions. Table 4 presents summary statistics on the
subsample used in the estimation procedure, which are roughly in
line with the entire (table 2). In addition, the public use SCF
data set contains five implicates of the data. The binomial probit
results reflect the estimated results corrected for imputation
variance. The ordered probit and multinomial logit results reflect
results from the first data implicate only. Results from the other
data implicates are qualitatively similar.20 Finally, the SCF oversamples
relatively wealthy families.21 Although the data include weights that
could control for this data feature in the estimation, the
nonlinearities of the model prevent them from being used
effectively. In order to check how the sample affects the results,
the models were run on subsamples that eliminated families with
greater than $3.25 million in assets or $400,000 in income in 2001
dollars.22 This subsample contained 3,260
families in 2001, 3,231 families in 1998, and 3,273 families in
1995. In what follows, the results for the subsample are
qualitatively similar, but in some instances, significance of
parameter estimates change. In order to aid comparability across
time, all results are in 2001 dollars.

Binomial probit results

The first part estimates binomial probits of the probability of
using or having debit cards, credit cards, direct payment and
checks. It uses the EM algorithm, and is estimated using maximum
likelihood techniques.23 The probability of using or holding
one of these instruments depends on consumer characteristics from
one of three groups. The first group is financial characteristics -
income, number of financial institutions, and homeownership. The
second group is demographic - age of head, education, number of
children, marital status, female headed household, or ethnicity.
The third group reflects employment status - self-employed,
retired, number of years with employer, and an indicator of the
number of years with employer being less than one. Tables 5 (a)
through (d) report the binomial probit results. The first column of
figures under each year is the parameter estimates, the second
column is the marginal effect of the variable. For continuous
variables - log income, squared log income, number of institutions,
number of children, number of years with employer - the marginal
effect is the average across observations of the derivative of the
probability with respect to the variable. In other words, one takes
the parameter estimates and calculates each observation's marginal
probability with respect to income. These marginal probabilities
are then averaged across observations. For the dummy variables, the
marginal effect is calculated as the average of the differences
across observations between the probability of using or having with
the dummy variable set to one, and set to zero.

Across all years, higher income families seem more likely to use
debit cards, but the negative coefficient on the square of log
income indicates that this use rate increases at a decreasing rate.
This observation is consistent with the simple plot in figure 1(a),
where debit card use rises, then falls with income. A family likely
needs a certain level of income in order to have general access to
financial services, but as income rises, families may start to
substitute other forms of payment for debit cards. As discussed
below, wealthier consumers may substitute convenience use of credit
cards for debit cards.

More education also leads to a higher probability of debit card
use. Although income and education are correlated, these two
variables have separate effects in the specficiation. In a study of
young Finnish consumers, Hyytinen and Takalo (2004) found that more
informed consumers are more likely to use newer forms of payment.
The education result here could be broadly consistent with this
phenomenon.24

The older age category dummies have negative coefficients, which
implies that younger families are more likely to use a debit card
than older families. In 2001, the coefficient on nonwhite is
positive and significant. Except for the 1995 survey,
self-employed, retired, and number of years with employer are
negatively correlated with the probability of using a debit card.
These could be isolating effects due to income and age that are not
picked up by these other variables. Tests show that the data have
significant multicollinearity; thus the results should be
interpreted as broadly indicating that debit cards are generally
used by higher income, younger, and more educated families.25

The marginal effects reported in the last columns indicate that
a one percent change in income and age lead to larger changes in
the probability of using or holding these payment instruments than
the other variables. The magnitude of the income effect decreases
over time, while the magnitude of the age effect increases. The
pseudo-R squared statistics indicate that these variables explain a
modest amount of the variation in debit card use. However, this
variation seems to be better explained in later years; in 2001, the
level of this statistic reaches over ten percent. Supply factors
may explain some of the variation in earlier years, but it is
difficult to test this hypothesis with the available data.

Turning to bank credit card holdings, the coefficient on log
income is positive and significantly different from zero in all
survey years, while the coefficient on non-homeowner is negative
and significant. Both of these variables point to the importance of
income and assets as determinants for bank credit card holdings.
More education indicates a higher credit card holding rate, and the
number of children and nonwhite families indicate a lower holding
rate.26 In contrast to the debit card results,
the retired variable is not significantly different from zero in
all survey years.

Convenience use of credit cards is positively correlated with
age and education. This is an interesting contrast to the debit
card results, which indicate that debit card use is negatively
correlated with age, possibly suggesting that older families tend
to be less credit constrained than younger families. Consistent
with this view is that retired families are more likely to be
convenience users, and non-homeowners are less likely. It may also
reflect cohort differences in attitudes towards debit cards.

Using direct payment is positively correlated with income across
all years in the sample. Interestingly, older families seem
significantly less likely to use direct payment in the earlier
years of the sample but not in the later years. This could point to
significant supply effects for some types of payments; for example,
more insurance companies or utilities may have started to offer
direct payment to all customers. Similar to other electronic
payment use, education is positively correlated with direct payment
use, but nonwhite families are less likely to use direct payment.
Renters seem less likely to use direct payment. In general,
mortgages may be paid with electronic payments, but rent payments
are less likely to be paid electonically. The amount of variation
explained in the data by these variables seems modest, as shown by
the pseudo R-squared statistic.

The final table shows the results from estimating the
probability that families use a check as a main way to do business
with a financial institution. Similar to debit card use, income and
higher education are significantly positively correlated with check
use. However, similar to credit card use, nonwhite and nonhomeowner
status are significantly negatively correlated.

Importantly, the binomial probit results and the binomial logit
results are generally qualitatively similar, indicating that the
results are relatively robust to distributional assumptions.

Ordered probit results

Table 2 (b) presented summary statistics suggesting a rise in
multihoming over the sample period. In order to investigate this
phenomenon more thoroughly, tables 6(a), (b) and (c) present
results from estimating an ordered probit for the number of payment
instruments used in 1995, 1998, and 2001. The four payment
instruments examined are debit cards, credit cards, direct payment,
and checks in 1998 and 2001, and the three payment instruments
examined in 1995 are debit cards, credit cards, and direct payment.
The explanatory variables are the same as were used in section
4.1.

Similar to the binomial results, the characteristics that
explain multihoming behavior are relatively constant across time.
The number of payment instruments used is positively correlated
with income, which could proxy for differential access to financial
services across the income distribution. Age is negatively
correlated with multihoming. This could point to increased adoption
behavior by younger families than by older families. Unmarried
hourseholds are less likely to multihome, potentially indicating
different payment preferences within a household.27 Non-homeowners are less likely to
multihome; this could be a result of the fact that many mortgages
are paid with direct payments, and thus, increase the number of
payments used by any family. The self-employed are less likely to
multihome; other researchers have found evidence that the
self-employed differ somewhat in payment preferences from the
general population.28

In general, the results suggest that the adoption of debit cards
by young families over the period did not imply completely
eliminating other forms of payment. Although not directly estimable
from these data, the results are consistent with families holding
multiple payment instruments, using one for its best suited
purpose. The next section investigates the correlation between
familly characteristics and using different pairs of payment
instruments.

Multinomial logit results

The final step in the analysis is to see what factors affect the
decision to hold multiple payment instruments and to understand how
the decisions to use or hold multiple payment instruments are
correlated. To this end, joint choices of payment instruments are
constructed, and the estimation procedure assumes that families
choose the one that maximizes their utility. As explained in
section 3.2 the estimation procedure uses
only a subset of the potential combinations. The tables report
estimation results on the decisions to use debit cards and to hold
credit cards; decisions to use debit cards and to be convenience
users; decisions to use debit cards and to use checks as a main way
to interact with a financial institution; and decisions to use
direct payments and use checks as a main way to interact with a
financial institution. In each case, there are four possible
outcomes. For example, in the debit card, credit card choice the
outcomes are: do not use a debit card, do not use a credit card; do
not use a debit card, use a credit card; use a debit card, do not
use a credit card; and use a debit card, use a credit card. The
specification uses the "do not use" both instruments as the
normalized outcome, and the reported coefficients are relative to
this outcome.

The reported results show how family characteristics are
correlated with the use or holdings of these combinations of
payment instruments. The specification assumes that the unobserved
part of utility is distributed with a multinomial logistic
distribution. Because the logistic distribution exhibits the
independence from irrelevant alternatives property, estimation
results on a subset of the possible combinations lead to the same
odds ratios as estimation results on all of the possible
combinations.

Tables 7 (a) through 7 (k) report the results.29 The first column under each year
reports the parameter estimate, the second reports the standard
error, and the third reports the marginal effect of the variable.
These are calculated as the change in the marginal probability of
use or holding with a change in the independent variable. The
parameters used to evaluate these changes are the estimated
parameter minus the mean of the parameters across choices. Thus, it
is possible that a reported coefficient and a marginal effect have
different signs.

In general, the results reveal the following trends. Across all
combinations, debit card use is generally negatively correlated
with age, and positively correlated with education. In most cases,
these correlations are significant. Married families are more
likely to use more than one instrument than nonmarried families,
and homeowners are more likely to use more than one instrument than
nonhomeowners. These results are consistent across time. The
married results may point to differences in preferences within a
family, although given the data construction, it is difficult to
tell. Homeowners most likely use direct payment for a mortgage, and
this would cause an increase in the number of instruments a family
uses or holds, all other things equal.

The most striking difference in the multinomial results from the
binomial results are the income results. In some cases, the
multinomial income coefficients are negative, while they are
positive in similar binomial results. There are a few potential
explanations for this difference. As explained above, the SCF
oversamples wealthy families. Interpreting income coefficients
without sample weights can be difficult, but using sample weights
in nonlinear estimation routines can be problematic. In addition,
in some of the specifications, one of the choices - using a debit
card, but not using the other instrument - has a small number of
respondents in each survey year. For example, in the debit card,
credit card choice results, in 2001, debit card only users
represented 316 families, or an unweighted 7.48 percent of the
sample; in 1998, 232 families or an unweighted 5.70 percent of the
sample, and in 1995, 100 families, or an unweighted 2.48 percent of
the sample. Thus, the coefficients may need to be interpreted with
care. Moreover, there is significant multicollinearity in the data.
Because there are many more parameters to estimate in the
multinomial specification than in the binomial specification, the
multicollinearity in the data may contribute to the sign changes
for some of the parameters.

In order to evaluate the substitutability of different payment
instruments, the next step was to estimate a nested logit model.
The nests were formed as follows.30 Using neither of the pair of payment
instruments and using both of the payment instruments were each
their own nests, while using one or the other payment instrument
were nested. This lends insight into how families multihome.
Specifically, an inclusive parameter in the nested logit that is
significantly different from and less than one will indicate that
families view the two payment instruments as an either-or decision.
Either they use one payment instrument, or they use the other
payment instrument. Alternatively, an inclusive parameter that is
not significantly different from one indicates little difference
between the nested logit model and the multinomial logit model,
implying no discernable pattern between choosing neither,
either-or, or both payment instruments. An inclusive parameter
greater than one, although somewhat at odds with theory, possibly
indicates that families may be more likely to use both of the
payment instruments.

Accordingly, as shown in Table 8, the results suggest that using
debit cards and credit cards were viewed as an either-or decision
in 1995, but then grew to a both decision in 2001. Dividing this
result further suggests that families view debit card and
convenience use of credit cards as an either-or decision. The debit
and check use results suggest no regular pattern, as the nested
multinomial logit model cannot be distinguished from a multinomial
logit model. Together with the direct payment and check use result
in the last line of the table, these results suggest that there may
be less systematic variation in families' preferences for check
writing, or more likely, it is difficult to uncover systematic
preferences for check writing using these data. The debit card and
direct payment results suggest that families view debit card use
and direct payment use as an either-or decision; however, the
standard errors on these estimates are fairly large and thus the
results are not easily interpreted.

Conclusion

This paper shows that families' use and holdings of payment
instruments depends critically on their income, age, and
demographic characteristics. Despite significant increases in the
levels of use and holdings, the family characteristics that predict
use and holdings of each instrument are generally the same across
time. This paper first shows that payment use and holdings are
significantly correlated with consumer characteristics, and showed
that these results are consistent across time. It also documents
the rise in multihoming, providing insight into the factors that
predict multihoming by families. With that information in mind, it
estimated joint decisions to use and hold different payment
instruments. This is an important exercise, as many families hold
more than one of each of these payment instruments.

In general, families that are younger, higher income, and better
educated are more likely to use electronic payment instruments, and
more than one payment instrument. The patterns of substitution
across payment instruments differ. Most notably, debit card use and
convenience credit card use seem to be strong substitutes, while
other combinations of payments do not exhibit these tendencies. In
future research, it would be interesting to explore these
substitutions further, to see if more complete data provides
additional insight into consumer payment behavior.

Consumers and businesses may continue to substitute electronic
payments for check payments in the future. Most importantly, the
shift in payments from paper to electronics represents a societal
change in the way that people go about their every day business.
For years, industry participants have waited for "the checkless
society". The data indicate that while not here, the checkless
society may be speeding its approach. It is important to understand
family-level behavior in light of this signficant overall change in
the U.S. payment system.

Acknowledgments

I thank Kenneth Kopecky, two anonymous referees, and David Van
Hoose for thoughtful comments on the paper. I also thank Geoff
Gerdes, Diana Hancock, Kathleen Johnson, Jeff Marquardt, David
Mills, Kevin Moore, Travis Nesmith, Bill Nelson, Leo Van Hove,
Jonathan Zinman and seminar participants at the the Federal Reserve
Bank of Philadelphia and the Eastern Economic Association for
helpful comments and suggestions. I also thank Dan Dube and
Namirembe Mukasa for excellent research assistance.

Appendix: Survey of Consumer Finances Questions

The SCF contains both direct and indirect questions on payment
choices. Respondents answer direct questions with "yes", "no" or
"not applicable". The indirect questions ask respondents to name
the "main ways" they interact with financial institutions.
Respondents may answer these questions by choosing from a list of
potential responses on the screen, or choose another response.
Respondents may also choose more than one response.

While the debit card use, credit card holdings and direct
payment use direct responses, the check use statistics use the
indirect responses from the "main ways" question. The 1998 and 2001
waves of the Survey include check use in the provided responses,
but not in the 1995 wave.31 Thus, although the data do not measure
check writing directly, this measure may be correlated with check
writing. The statistics reported in this paper should be
interpreted with these differences in mind.

Below, a * indicates a reponse provided to the survey
respondent.

Direct questions: 1995, 1998, 2001

A debit card is a card that you can present when you buy things
that automatically deducts the amount of the purchase from the
money in an account that you have.

Do you use any debit cards? Does your family use any debit
cards?

INTERVIEWER: WE CARE ABOUT USE, NOT WHETHER R HAS A DEBIT
CARD

1. *YES

5. *NO

Indirect questions: 1998, 2001

(SHOW CARD 4) What are the main ways (you do/your family does)
business with this institution [-by check, by ATM (cash machine),
by debit card, in person, by mail, by talking with someone on the
phone, by touchtone service on the phone, by direct deposit or
withdrawal, by computer or online service, by other electronic
transfer, or some other way]? Please start with the most important
way.

CODE ALL THAT APPLY: CODE MAIN METHOD FIRST AND REMAINDER

IN ORDER GIVEN

1. *CASH MACHINE/ATM/debit card

2. *IN PERSON

3. *MAIL

4. *PHONE - TALKING

5. *DIRECT DEPOSIT

6. *DON'T DO REGULAR BUSINESS

7. *PHONE - USING TOUCHTONE SERVICE

8. *DIRECT WITHDRAWAL/PAYMENT

9. *OTHER ELECTRONIC TRANSFER

10. *CHECK

11. R's agent or manager; personal banker; go-between (this is a
broad category that encompasses both formal and informal
relationships)

"Replacement of Cash by Cards in US Consumer
Payments," Journal of Economics and
Business, forthcoming.

Humphrey, David B. and Berger,
Allen N. (1990.)

"Market Failure and Resource Use: Economic
Incentives to Use Different Payment Instruments," in The U.S. Payment System: Efficiency, Risk and the Role of
the Federal Reserve, Federal Reserve Bank of Richmond,
Kluwer Academic Publishers, 45-86.

Hyytinen, Ari and Takalo, Tuomas. (2004.)

"Multihoming in the market for payment media:
Evidence from young Finnish Consumers," Bank of Finland Discussion
Papers, no. 25.

1. Board of Governors of the
Federal Reserve System, Mail Stop 75, 20th and C Streets,
Washington, DC 20551. Tel: (202) 721-4501. Email:
elizabeth.klee@frb.gov. The views expressed in this paper are those
of the author and not necessarily those of the Board of Governors,
other members of its staff or the Federal Reserve System. Return to Text

2. Automated clearing house
(ACH) payments transfer money electronically from one bank account
to another bank account. Common uses include mortgage, utility bill
and insurance premium payments. Return to Text

10. All figures are in 2004
dollars. The U.S. Census Bureau defines e-commerce as "sales of
goods and services where an order is placed by the buyer or price
and terms of sale are negotiated over the Internet, an extranet,
Electronic Data Interchange (EDI) network, or other online system.
Payment may or may not be made online." In practice, it is likely
the case that payment for most consumer retail sales and some
percentage of the EDI sales are made electronically. Return to Text

11. Consistent aggregate
annual data on the number of check payments are not available. The
best recent data available are from surveys conducted by the
Federal Reserve System. Estimates developed from Federal Reserve
check surveys in 1995 and 2001 suggest that about 49.5 billion
checks were paid in the United States in 1995 and 42.5 billion in
2000. While the estimated number of checks paid is significantly
larger in 1995, the exact year that check use peaked is unknown.
This evidence suggests, however, that the number of checks declined
at an average rate of about 3 percent per year in the latter part
of the 1990s and early 2000s. See Gerdes and Walton (2002) for more
details. Return to Text

12. The decline in the total
real value of payments from 1998 to 2001 may be due to an
assumption of a constant real dollar value of a check. Estimates
from the Federal Reserve check survey indicate that the average
value of a check was $925 in 2000. This implies that the average
value of a check in 2001 dollars was approximately $951. The
estimate of the real dollar value of check payments in 1998 is
derived by holding the average check value constant from 1998 to
2001. But, if consumers substituted debit cards or other payment
methods for relatively low-dollar value checks from 1998 to 2001,
it may be the case that the average check value for 1998 should be
lower. Return to Text

13. The SCF surveys a
cross-section of U.S. households, and is conducted triennially by
the Federal Reserve in conjunction with the National Opinion
Research Center at the University of Chicago (NORC). The strength
of the SCF is its ability to report accurately demographic and
financial data. See Aizcorbe et. al (2003) for details. Return to Text

14. A " family" or "primary
economic unit" is defined as the "economically dominant single
individual and couple (whether married or living together as
partners) and all other persons in the household who are
financially interdependent with that person or persons." See
Aizcorbe et al. (2003). Return to
Text

16. Identifying check use in
the SCF is more complicated than identifying use of debit cards,
holdings of credit cards or use of direct payment. The check
results should be interpreted with this in mind. Appendix A
provides details. Return to
Text

17. Zinman (2005) looks to
neoclassical economics for explanations of these phenomena.
Return to Text

18. It should be noted that
the SCF does not contain information on these factors. Return to Text

24. This result is seen in
the broader literature on technology adoption - across countries
and across techologies. See Caselli and Coleman (2001), for
example. Return to Text

25. The test for
multicollinearity is defined by calculations of the condition
number defined by Belsley et al. (1980). The condition number is
calculated as the square root of the ratio of the largest to the
smallest eigenvalue of the independent variables matrix,
normalizing the independent variables to be unit length vectors.
Complete independence yields a condition number of one. Belsley et
al. state that condition numbers over 100 are not uncommon in
econometric analysis, but indicate significant collinearity. The
condition numbers for 1995, 1998 and 2001 data sets are
approximately 246, 231 and 266, respectively. Return to Text

26. Duca and Whitesell
(1995) also find that income, age and demographic characteristics
are significantly correlated with credit card holdings. Return to Text

27. Research by
Borzekowski, Kiser and Ahmed (2005) shows that women may rank debit
cards higher as a payment choice than men do. Return to Text

29. The parameter estimates
and the marginal effects are averaged across all five implicates.
The standard errors are adjusted for variance across implicates.
All individual implicate results are qualitatively similar.
Return to Text

30. The methodology in this
section follows Bagley and Mokhtarian (1997). Return to Text

31. The result of this
omission is that relatively few families reported using checks as a
main way to interact with a financial institution, though this was
likely not the case. Return to
Text

A** indicates that the estimated coefficient is significantly different from zero at the 95 percent confidence level.